Signal processing systems have the problem that they need to operate in conditions where the signal units are a priori unknown. In terms of images, we might observe a boy sitting under a shaded tree such that the difference in physical units between sunlight and shade is 100000 to 1. Yet, we do not have the capacity to work with such a large signal range.
Embodiments of the present invention are based on the proposal that standard coordinates are particularly useful in imaging. Let I(x,y) denote an image brightness at location x and y. The logarithm of the image response is denoted i(x,y). The brightness and contrast of I can be changed by a linear transform if i: i(x,y)−mi(x,y)+b where m and b are scalings. The brightness term b scales the brightnesses in an image (b is a multiplicand in non-log space) and accounts for changes in the overall brightness of a scene. In terms of a trichromatic camera where the signal is composed of red-, green- and blue-records we have 3 images; R(x,y), G(x,y) and B(x,y) and there might be 3 individual brightness factors. For example the move to a bluish light from a yellowish one might be modelled by large blue- and small red-brightness factors. The contrast term m accounts for the number of log-units available. Consider taking a picture outside where the signal range is 100000 to 1. In contrast a photographic reproduction might have a signal range of 100 to 1, a shift in log-units of 5 to 2. Coding an image in terms of standard coordinates calculated for i(x,y)
e.g.
            i      ⁡              (                  x          ,          y                )              -          μ      ⁡              (                  i          ⁡                      (                          x              ,              y                        )                          )                  σ    ⁡          (              i        ⁡                  (                      x            ,            y                    )                    )      (μ and σ denote mean and standard deviation)
has two main advantages. First, it is invariant to μ and σ (so the z-scores for the photographic image and the outdoor signal are the same). This invariance might be useful for recognising signal content. Second, an image is recast in a way which makes sense in terms of our own visual perception. We as people see scenes with high dynamic ranges (100000 to 1) yet such a high dynamic range is not used in the cortex. Rather, areas in an image with widely different signal ranges are recoded into the same units. For example, the physical units in shadows and highlight regions are small and large respectively. Yet, if the image is coded in (local) standard coordinates the shadow units will become relatively bigger and the highlight coordinates relatively smaller. The import of this is that we can see into shadows and into highlights. This tallies with our experience as human observers. Recoding images in terms of standard coordinates provides an elegant solution to a signal-processing problem with which our own visual system must contend.